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Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry)
Constant factor rule in integration; Linearity of integration; Arbitrary constant of integration; Cavalieri's quadrature formula; Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution
Implicit function theorem; Increment theorem; Integral of inverse functions; Integration by parts; Integration using Euler's formula; Intermediate value theorem; Inverse function rule; Inverse function theorem
The theorem is a special case of the polynomial remainder theorem. [1] [2] The theorem results from basic properties of addition and multiplication. It follows that the theorem holds also when the coefficients and the element belong to any commutative ring, and not just a field.
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: =. That difference is algebraically factorable as (+) (); if neither factor equals one, it is a proper factorization of N.
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function. The first part of the theorem, sometimes called the first fundamental theorem of calculus , states that one of the antiderivatives (also called indefinite integral ), say F , of some function f may be ...